All eyes were on Cesc Fàbregas at the start of this match: such an excellent signing in his brief Chelsea career to date but apparently not required at Arsenal this summer, for all his own occasionally mawkish declarations of enduring Gunner-dom. Football can be a hilarious business at times, a Jeremy Kylie-ish fudge of bolt-on loyalties and hysterically conceived betrayals. Here two months into his Chelsea career Fàbregas was booed by Arsenal’s fans on his first few touches of the ball, drawing a supportive answering jeer from the home crowd.

And yet there was by the end a kind of clarity about Arsène Wenger’s decision not to re-sign his former captain, on an afternoon where Wenger himself became the story to a degree. Not just for Fàbregas-related reasons but for his part in a ludicrous and appallingly-timed shoving match with José Mourinho on the touchline midway through the first half. “I wanted to head from A to B and I was interrupted,” Wenger said, explaining he was going to check on Alexis Sánchez, who had just been fouled. It is a nice line, but also, on balance, a fairly accurate description of his team’s approach to these occasions on the field. Once again Arsenal tried, in their own flowing, frictionless way, to proceed from A to B against a high pressure, physically robust elite level team. Once again they were interrupted.

Fàbregas, for his part, had a busy and effective game, ferreting about profitably and providing the sublime lofted pass through a vacant Arsenal defence that allowed Diego Costa to show his ruthlessness in front of goal and complete a 2-0 win for Chelsea. It would be wrong to conclude, on this evidence, that Wenger blundered unforgivably in failing to re-sign Fàbregas. Blundered in other areas perhaps: but if Arsenal have now collected 26 points out of a possible 93 against the Premier League’s Champions League teams over the last five years this is not for the lack of a deep-lying passer, or a dearth of fine-touch playmakers (although Fàbregas would no doubt be an upgrade in that area).

In reality the player Arsenal fans would be best served taking out of this Chelsea team is not Fàbregas but Nemanja Matic, who was by some distance the most physically imposing midfielder on show, telescopically quick to the ball, able to pass short or long, aggressive but, above all, always in control.

Whereas Arsenal, and their manager during that rather dismal altercation, looked at full stretch. There is a theory their rash of injuries is a function of overcompensation, of players built to provide craft being asked to fight and hustle as well: referred pain from a lack of muscle elsewhere. Here they showed a similar kind of compensatory aggression. There had already been some early roars of outrage at Arsenal’s – yes Arsenal’s – strong arm – yes strong arm – tactics when, with 20 minutes gone, Mathieu Flamini hustled Oscar to the floor, drawing in return a heavy tackle by Gary Cahill on Sánchez by the touchline.

At which point: enter Wenger. Rising from his dugout – and he is a startling figure on these occasions, impossibly tall, arms flapping like deckchair struts – Wenger walked across in front of Chelsea’s technical area and shoved Mourinho two-handed in the chest. It was a slightly jaw-dropping moment. Wenger was reacting to some verbal provocation from Mourinho, who was phlegmatic about the whole thing afterwards. It is still hard to avoid the conclusion that feistiness both on and off the field was all of a piece, an assumed aggressive attitude that was only ever likely to hold together for so long.

Seconds later Calum Chambers was booked (a tautology: Chambers is, unless explicitly stated otherwise, pretty much always in the process of being booked) for tripping Eden Hazard. And shortly after that the game turned on a moment of craft and a brief glimpse of that familiar collapsibility. First Hazard dipped inside Santi Cazorla, who is no central midfielder, with laughable ease 30 yards from goal. Then he swept past Chambers, tentative having been booked, with a disdainful little switch of the hips. Finally he drew a lunge from Laurent Koscielny that sent him tumbling for an obvious penalty, which Hazard rolled into the corner with a delicious little side-foot.

It was in its own way a very funny decisive five minutes of football. Arsenal’s manager goes toe-to-toe with his opposite number on the touchline in order to show his team will not – repeat will not – lie down in front of Chelsea this time around: and two minutes later Arsenal proceed to lie down in front of Hazard’s driving run and the game is all but gone.

“We’ve got Cesc Fàbregas” Chelsea’s fans chanted by way of a taunt as the players left the field but Fàbregas isn’t the most obvious missing piece in this Arsenal team. Similarly Chelsea didn’t win here because of Arsenal’s failings. They won because, among other things, Hazard had a superbly composed and incisive game drifting across from his inside-left position. Because of the excellence, poise and – yes – muscle of Matic in the spine of the team. And because Chelsea looked what they are here, the Premier League’s most obviously complete first XI, and a team who, in contrast with their opponents, tread a comfortable line between craft and muscle.